H-infinity filter design for nonlinear systems with quantised measurements in finite frequency domain
Résumé
This paper deals with the problem of finite frequency (FF) H-infinity full-order fuzzy filter design for nonlinear discrete-time systems with quantised measurements, described by Takagi-Sugeno models. The measured signals are assumed to be quantised with a logarithmic quantiser. Using a fuzzy-basis-dependent Lyapunov function, the finite frequency l(2) gain definition, the generalised S-procedure, and Finsler's lemma, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H-infinity attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. With the aid of Finsler's lemma, a large number of slack variables are introduced to the design conditions, which provides extra degrees of freedom in optimising the guaranteed H-infinity performance. This directly leads to performance improvement and reduction of conservatism. Finally, we give a simulation example to demonstrate the efficiency of the proposed design method, and we show that a lower H-infinity attenuation level can be obtained by our developed approach in comparison with another result in the literature.